Topological Origin of Holographic Principle: Application to wormholes

In this paper, we suggest a mathematical representation to the holographic principle through the theory topological retracts. We found that the topological retraction is the mathematical analogs of the hologram idea in modern quantum gravity and it can be used to explore the geometry of the hologram boundary. An example has been given on the five dimensional (5D) wormhole space-time $W$ which we found it can retract to lower dimensional circles $S_i \subset W$. In terms of the holographic principle, the description of this volume of space-time $W$ is encoded on the lower-dimensional circle which is the region boundary.